Exercise 1 *Problem 4.2 Use separation of variables in cartesian coordinates to solve the infinite cubical well (or "particle in a box"): 0, if x.y. z are all between 0 and a: 0o, otherwise. (x. y. z) = (a) Find the stationary states, and the corresponding energies. (b) Call the distinct energies E1. E2. E3, .., in order of increasing energy. Find E1. E2. E3, E4. Es, and E6. Determine their degeneracies (that is, the number of different states that share the same energy). Comment: In one dimension degenerate bound states do not occur (see Problem 2.45), but in three dimensions they are very common. (c) What is the degeneracy of E14, and why is this case interesting?

Exercise 1 *Problem 4.2 Use separation of variables in cartesian coordinates to solve the infinite cubical well (or "particle in a box"): 0, if x.y. z are all between 0 and a: 0o, otherwise. (x. y. z) = (a) Find the stationary states, and the corresponding energies. (b) Call the distinct energies E1. E2. E3, .., in order of increasing energy. Find E1. E2. E3, E4. Es, and E6. Determine their degeneracies (that is, the number of different states that share the same energy). Comment: In one dimension degenerate bound states do not occur (see Problem 2.45), but in three dimensions they are very common. (c) What is the degeneracy of E14, and why is this case interesting?